1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to a method for determination of formation resistivity using multi-array resistivity data.
2. Background of the Art
Electromagnetic induction, wave propagation, and galvanic logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al. Other tools include the HDLL (High Definition Lateral Log) of Baker Hughes Incorporated, described in U.S. Pat. No. 6,060,885 to Tabarovsky et al., and any generic Array Laterolog tools, e.g., the High Resolution Laterolog Array tool (HRLA) of Schlumberger Inc.
Analysis of measurements made by an array induction logging tool such as that disclosed by Beard and galvanic logging tools such as the HDLL and HRLA or any generic Array Laterolog tools are based on inversion. Prior art log inversion methods commonly use a single formation model for the entire interpretation process. This single model approach has limitations when executing either joint or sequential inversions.
One problem with inversion is that the earth is characterized by, at the very least, a 2-D model (layers with radial changes in resistivity within each layer). A rigorous 2-D inversion technique would be quite time consuming and impractical for wellsite implementation. See, for example, Mezzatesta et al., and Barber et al. Several methods have been used in the past for speeding up the inversion. One method is based on a sequential determination of the formation parameters. See, for example, Frenkel et al. (2004). Another method is to get a better initial model determination. This is discussed with reference to high definition lateral logs by Hakvoort et al. or Frenkel and Walker (2001). Yet other methods divide the multidimensional (2-D or 3-D) inversion process into a sequence of simple one-dimensional processes. See for example, U.S. Pat. No. 5,889,729 issued to Frenkel et al., Frenkel et al. (1996), and Frenkel (2002) disclose a rapid inversion method that performs a sequence of 1-D iterations that converge to the true 2-D or 3-D isotropic or anisotropic solution.
The so called 1-D+1-D method of Griffiths et al. is based on sequential vertical 1-D (shoulder-bed correction) and horizontal (radial) 1-D inversions. The main shortcoming of this method, as indicated by the authors, is it may provide incorrect results for the thin invaded formations. Therefore, to complete the interpretation, an additional, time consuming rigorous 2-D inversion step is required.
It should be noted that the referenced inversion-based array log data interpretation methods use a single formation model. By not accounting for the vertical resolution differences of the input subarray data, both joint or sequential inversion procedures may lead to unstable and incorrect results in thin invaded formations. A so-called multiscale inversion approach has been used for seismic data interpretation (see, for example, Bunks et al., and Zhou), but has not been applied to join inversion of well logs with different resolution.
There is a need for a 2-D and 3-D robust methods of interpretation that addresses the instability problems associated with thin bed inversion, accounts for different resolution of different log measurements, and is still computationally fast. The present invention addresses this need.